中文摘要：

通过对代数次数增加情况的分析，研究了type-1广义Feistel结构下，单SP（substitution-permutation）模型与双SP模型抵抗高阶差分分析的能力。结合高阶积分与高阶差分思想，开发了四路type-1广义Feistel-SP与Feistel—SPSP结构代数次数上界估计的新方法。利用这一方法，分别构造了这2种结构在2种常用参数下的区分器。结果显示，四路type-1广义Feistel结构下，双SP模型抵抗高阶差分攻击的能力不如单SP模型；

英文摘要：

The powers against the higher-order differential cryptanalysis of the single-SP（substitution-permutation） model and the double-SP model are studied in the type-1 Feistel network by analyzing the growths of algebraic degrees. Combining the higher-order integral and the higher-order difference, a new method is exploited to estimate the upper bounds of algebraic degrees for the 4-line type-1 Feistel-SP scheme and the 4-line type-1 Feistel-SPSP scheme. Applying the new method, distinguishers of the two schemes are constructed with four common parameters. As a result, the dou- ble-SP model is weaker than the single-SP model against the higher-order differential attack under the 4-line type-1 Feistel structure.